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Search: id:A004135
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| A004135 |
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Additive bases: a(n) is the least integer k such that in the cyclic group Z_k there is a subset of n elements all pairs (of distinct elements) of which add up to a different sum (in Z_k).
(Formerly M0782)
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+0
3
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| 1, 2, 3, 6, 11, 19, 28, 40, 56, 72, 96, 114, 147, 178
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs, SIAM J. Algebraic and Discrete Methods, 1 (1980), 382-404.
H. Haanpaa, A. Huima and P. R. J. Ostergard, Sets in Z_n with Distinct Sums of Pairs, in Optimal discrete structures and algorithms (ODSA 2000). Discrete Appl. Math. 138 (2004), no. 1-2, 99-106.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. L. Graham and N. J. A. Sloane, On Additive Bases and Harmonious Graphs
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EXAMPLE
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a(4)=6: the set {0,1,2,4} is such a subset of Z_6, since 0+1, 0+2, 0+4, 1+2, 1+4 and 2+4 are all distinct in Z_6; also, no such 4-element set exists in any smaller cyclic group.
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CROSSREFS
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Cf. A004136, A004133.
Sequence in context: A032156 A146385 A039827 this_sequence A090036 A024971 A038084
Adjacent sequences: A004132 A004133 A004134 this_sequence A004136 A004137 A004138
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KEYWORD
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nonn,nice,more
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms and comments from Harri Haanpaa (Harri.Haanpaa(AT)hut.fi), Nov 01 2000
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